Problem: $f(n)=5\cdot(-2)^{{\,n-1}}$ Complete the recursive formula of $f(n)$. $f(1)=$
Solution: From the explicit formula, ${5}\cdot({-2})^{n-1}$, we can tell that the first term of the sequence is ${5}$ and the common ratio is ${-2}$. This is the recursive formula of the sequence: $\begin{cases} f(1)={5} \\\\ f(n)=f(n-1)\cdot({-2}) \end{cases}$